Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n ≥ 2 people are at a gathering. Every person shakes hands with every other person, but not themselves. Then, the number of total handshakes which occur is

Q: Find the Inverse Fourier transform of e) e 2 cw-4Jj 4- C4-wJj

A: Given: In this question, the given details are Here, the given expression is, e2(ω-4)j4-(4-ω)j To…

Q: Q4/ Find the inverse of Z-transform if 2(z2+z) x(z) =7-1,5z+0,5

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Q: Find the given inverse transform: L-1 1 s3+5s.

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Q: 5. Show the congruence axiom C3 for II (don't assume the field is Pythagorean)

A: To prove: The congruence axiom C3 for ΠF.

Q: Prove that (1, 2) (1,(1), 2, 3).

A: We know, if A and B are two sets then, A is subset of B  if every element in A is also in B.

Q: -3 -1 -2 Use the Gauss-Jordan method to find the inverse of A = 7 or 3 2 -4. show that A is not…

A: We will use Gauess-Jorden  method to find the inverse of matrix. In this method we put the the given…

Q: The Inverse Fourier transform for e(2-6)i is 5-(3-w)t O 2H(t +2)e 10-(5–31)t OH(t+2)e 10+(5-31)t O…

A: We need to find the inverse Fourier transform of e2w-6i5-3-wi The inverse Fourier transform of 1wi+a…

Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: z+1 (i)Find all possible expansion of about z = 0. z2 -z-2 (ii) Expand f(z) = e² about z = Tİ.

A: For part 2 Let z=u+(pi)i then expand wrt to u Then replace u as z-(pi)i

Q: Explain fermat's little theorem.

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Q: Find z-transfrm for (n-1) X(n) u(n-1) x (n) 5nucn) - 2 n (o.3) uci) 2)

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Q: rom the Fourier expansion of f(x) = {(1– x)? 0<x<1 t

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Q: - 34 as f(4)= ė" ult-1) Solve it in fourier transformation

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Q: Show by universal generalization (twice-applied) ((CC-A) AB) U (DNB)) = (BN((C-AJUD)).

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Q: 19. Is Q[x]/(x² – 6x + 6) a field? Why?

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Q: 2. (a) For n 2 0 write out the fint four terms of the sequence z(n) 3(-3)" and then use the…

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Q: Compute the coefficient Fourier an of the *-1, 0<r <a S(2) = { 0, *<I< 27

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Q: 2. Show that Q√3 = {a+b√3|a, b = Q} is a field by verifying the field axioms one by one.

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Q: F is sigma-field ACN FA = {AN B : B E F} %3D Question: Is FA sigma-field?

A: F is sigma field .

Q: Prove that (a) P(En F) = P(E)- P(En F) (b) P(EnF) =1-P(E) – P(F) + P(En F)

A: Solution: 6. Here, it is needed to prove that

Q: The algebra of differential operators closely resembles the algebra of ordinary real polynomials.…

A: True

Q: Prove Theorem| 2.3: (i) (A+ B)" = A" + B", (i) (A")" = A, (iii) (kA)" = kA".

A: To prove the given transformations

Q: tind the inuerse 2 franst of 之ー

A: Inverse z transform

Q: (a) The matriz 1 3 -1 0 5 3 0 2 is invertible. Find A- by any method you know.

A:

Q: Let A = [-6, 8) U [10, ∞). Ext(A) = ?

A: The given set .The aim is to find the exterior of the set .

Q: Could you derive the equation from this for βi that is used by the Newton algorithm

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Q: 더 - C 1 -2s +6 s+2 82 - 4s + 8+1 C S-2 1

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Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Find the given inverse transform L .((무) + (+) - (주) } { s2 S-2 O t+1+e2t O t– 1– e2t O t+ e2t…

A: Given that L−11s2−1s+1s−2. We have to find the inverse Laplace transform. Use formula L−1n!sn+1=tn…

Q: Find the function with the transform 10 1 - e-4s – 4se- â(s) = 1- e-10s

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Q: 3. There are three distinct cube roots of any nonzero real number c. (a) Set up an algebraic…

A: Sol:- (a) To find the three distinct cube roots of a nonzero real number c, we can set up the…